Role of the Buddhist in preserving the original teachings

For a start, there's the parable of the blind men and the elephant. Access To Insight describes this as

The Buddha's famous simile of the blind men and the elephant, illustrating the futility of arguing about one's views and opinions.

My characterization of it is that when you don't see the whole Dhamma, then hearing people each describe one portion/aspect of Dhamma sounds as if their descriptions might be mutually contradictory.

IMO the fact that they sound contradictory doesn't prove that they are for sure, because Dhamma is complicated (albeit skillfully summarized in the four noble truths).

Another important aspect to the sutta is I think that we should try to avoid this kind of behaviour:

And they kept on arguing, quarreling, & disputing, wounding one another with weapons of the mouth, saying, "The Dhamma is like this, it's not like that. The Dhamma's not like that, it's like this."

I think that's important e.g. because the title of the Sutta is "Sectarians". If me and my brother had arguments or fights when we were young, my mother's policy (when she was called to resolve our dispute without knowing what the dispute was about) was that if we were fighting then we were both wrong.

If you feel the need to correct someone there are instructions related to Right Speech.

I may feel tempted to correct a "wrong concept", even without having been invited to.

Part of the (secular, non-Buddhist) way in which I've been taught to express disagreements is to use so-called "I-messages". For example, instead of a 'you-message' like "you are wrong", an 'I-message' like "I didn't understand that" is less aggressive and maybe closer to the truth (or at least closer to the way that leads towards understanding). So perhaps you can phrase any "corrections" as questions, "Where did the Buddha say that?", "Does that contradict this sutta?", etc.

Also there is the Parable of the burning house. I thought that this book might be like what you described, i.e. written or synthesized by the author without entirely quoting from suttas. According to the book, the author, "serves the congregation of Vipisanna Meditation Retreat in Willis, Texas, as its president while teaching English at the University of Houston-Downtown." The author is a bhikkhu and his congregation is presumably not.

The situation you mentioned is covered in the Drum Sutta.

The way to put this right is to learn the original teaching and practice it. When you build self confidence in the practice through experience teach what you practiced.

As long as there are people practicing and teaching the 4 foundation of mindfullness, the Dhamma shall endure.

Intellectual debate and corrections at the level of perception maybe of some help but would be limited as sometimes others may not agree because it is perceived by their intellect and perception than experience. When people has verified something at the experiential level the confidence is unshakable.

Ven. Yuttadhammo wrote in his answer:

Of course, the fact that the tipitaka is tens of times the size of the bible makes it relatively expensive to translate, print, ship, etc., and so it is not exactly the kind of thing you see in hotel rooms (for other reasons as well).

The above is precisely the reason why the Tipitaka is not as famous or as accessible to non-Buddhists as the Bible, Quran or the Bhagavad Gita. A lot of the sutta pitaka, have duplication due to the Buddha delivering the same messages to different people at different times in his 45 years of teaching. It is also not thematically arranged, at least for the most part. This and the sheer size of it, makes it less accessible to the non-Buddhist.

For this purpose, I recommend the book In The Buddha's Words by Bhikku Bodhi. It is an anthology or selection of translated suttas from the Pali canon. It is also thematically and systematically arranged. You can look at the Table of Contents on the Amazon page I linked. It is 512 pages long, which is quite alright. PDF version here. The author hopes that the book will serve as a systematic map to the Nikayas (which is like a jungle) for readers who are not yet well acquainted with the Pali canon.

When a Buddhist faces this situation, when he finds someone with a wrong concept, something that clearly has no basis on the Buddha's teachings, either Vinaya or Sutta Pitaka, what should he or she do? Should he/she correct the person or just let it be?

Well, if you are talking about books, then head over to amazon.com or goodreads.com and write your comments and vote down books which you think have wrongly represented Buddhist teachings. If many Buddhists do that, it would surely have an impact on the books' ranking.

I would go with "correct" however you will see that most Buddhist leaders don't do that

I'm not sure about "Buddhist leaders", but in general, I think that's not so much the case. Also, a lot of books are written precisely because of the presence of misleading books. To the point of having titles like Buddhism Is Not What You Think (though I never fully read this one, I find it unfortunate that, carrying such title, it barely and only loosely quotes the Buddha).

I think what a reasonable person should do in this case is what she would do in any other case, when circumstances are appropriate: point to contrary evidence.

there are lots of precautions to avoid long debates in Buddhism

If authoritative texts are available in one's language, and if one can refer people to evidence therein of faulty understanding, that should produce a very short debate, shouldn't it?

My understanding is that the major problem is not the availability of misleading books. Is the absence of authoritative books.